A Difference of Convex Functions Algorithm for Switched Linear Regression

作者：Tao Pham Dinh^*; Hoai Minh Le; Hoai An Le Thi; Lauer Fabien

来源：IEEE Transactions on Automatic Control, 2014, 59(8): 2277-2282.

DOI：10.1109/TAC.2014.2301575

• DC programming
• DCA
• nonconvex optimization
• nonsmooth optimization
• piecewise affine systems
• switched linear systems
• switched regression
• system identification

This technical note deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The technical note proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.

• 出版日期2014-8
• 单位INRIA